Introductory Combinatorics
by Brualdi, Richard A.Edition: 5th
Format: Hardcover
Pub. Date: 2008-12-28
Publisher(s): Pearson
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Summary
This trusted best-seller emphasizes combinatorial ideasincluding the pigeon-hole principle, counting techniques, permutations and combinations, Poacute;lya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, combinatortial structures (matchings, designs, graphs), and flows in networks. The Fifth Edition clarifies the exposition throughout and adds a wealth of new exercises.Appropriate for one- or two-semester, junior- to senior-level combinatorics courses.
Author Biography
Richard A. Brualdi is Bascom Professor of Mathematics, Emeritus at the University of Wisconsin-Madison. He served as Chair of the Department of Mathematics from 1993-1999. His research interests lie in matrix theory and combinatorics/graph theory. Professor Brualdi is the author or co-author of six books, and has published extensively. He is one of the editors-in-chief of the journal "Linear Algebra and its Applications" and of the journal "Electronic Journal of Combinatorics." He is a member of the American Mathematical Society, the Mathematical Association of America, the International Linear Algebra Society, and the Institute for Combinatorics and its Applications. He is also a Fellow of the Society for Industrial and Applied Mathematics.
Table of Contents
| What is Combinatorics? | |
| Example: Perfect Covers of Chessboards | |
| Example: Magic Squares | |
| Example: The Four-Color Problem | |
| Example: The Problem of the 36 Officers | |
| Example: Shortest-Route Problem | |
| Example: Mutually Overlapping Circles | |
| Example: The Game of Nim | |
| The Pigeonhole Principle | |
| Pigeonhole Principle: Simple Form | |
| Pigeonhole Principle: Strong Form | |
| A Theorem of Ramsay | |
| Permutations and Combinations | |
| Four Basic Counting Principles | |
| Permutations of Sets | |
| Combinations of Sets | |
| Permutations of Multisets | |
| Combinations of Multisets | |
| Finite Probability | |
| Generating Permutations and Combinations | |
| Generating Permutations | |
| Inversions in Permutations | |
| Generating Combinations | |
| Generating r-Combinations | |
| Partial Orders and Equivalence Relations | |
| The Binomial Coefficients | |
| Pascal's Formula | |
| The Binomial Theorem | |
| Unimodality of Binomial Coefficients | |
| The Multinomial Theorem | |
| Newton's Binomial Theorem | |
| More on Partially Ordered Sets | |
| The Inclusion-Exclusion Principle and Applications | |
| The Inclusion-Exclusion Principle | |
| Combinations with Repetition | |
| Derangements | |
| Permutations with Forbidden Positions | |
| Another Forbidden Position Problem | |
| Möbius Inversion | |
| Recurrence Relations and Generating Functions | |
| Some Number Sequences | |
| Generating Functions | |
| Exponential Generating Functions | |
| Solving Linear Homogeneous Recurrence Relations | |
| Nonhomogeneous Recurrence Relations | |
| A Geometry Example | |
| Special Counting Sequences | |
| Catalan Numbers | |
| Difference Sequences and Stirling Numbers | |
| Partition Numbers | |
| A Geometric Problem | |
| Lattice Paths and Schröder Numbers | |
| Systems of Distinct Representatives | |
| General Problem Formulation | |
| Existence of SDRs | |
| Stable Marriages | |
| Combinatorial Designs | |
| Modular Arithmetic | |
| Block Designs | |
| Steiner Triple Systems | |
| Latin Squares | |
| Introduction to Graph Theory | |
| Basic Properties | |
| Eulerian Trails | |
| Hamilton Paths and Cycles | |
| Bipartite Multigraphs | |
| Trees | |
| The Shannon Switching Game | |
| More on Trees | |
| More on Graph Theory | |
| Chromatic Number | |
| Plane and Planar Graphs | |
| A 5-color Theorem | |
| Independence Number and Clique Number | |
| Matching Number | |
| Connectivity | |
| Digraphs and Networks | |
| Digraphs | |
| Networks | |
| Matching in Bipartite Graphs Revisited | |
| Pólya Counting | |
| Permutation and Symmetry Groups | |
| Burnside's Theorem | |
| Pólya's Counting formula | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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